These two things are not friends with each other. For distance runners, they’re almost at-odds with one another. As a light runner, I don’t have issues, but I know others who long distance runners whose bodies need carbs while running have a hard time doing Paleo.
I don’t do the long distance stuff, so I won’t comment about that other than to say that I have read about Paleo people who do distance running, and while it’s a challenge, it’s do-able. I will talk about my own experience: running for fitness.
I run 5 miles or less typically every other day. On the days that I run, I do allow myself a little more food for breakfast, typically a piece of Paleo banana bread or maybe an extra slice of bacon. I find that my running doesn’t otherwise tax me otherwise. I don’t get hungrier, nor do I feel any other sort of discomfort.
Eating Paleo for someone like me doesn’t seem to have any detrimental effect on my running or my ability to keep running. The food fills me up and fuels me sufficiently to keep running. Since I’m only out running for 30-45 minutes at a time, my body doesn’t run out of fuel. At no point do I feel like I’m going to crash. I’ve never felt light-headed.
As far as water goes, I don’t drink before or during a run. Again, my runs are short, and the water fetish Americans have with hydration is really based more on marketing and less on real science. I don’t “re-hydrate” after a run, either. I drink normally at breakfast or dinner, whichever meal comes after my run. Again, I have experience no negative effects from this.
For someone who runs like I do, 3-5 miles every other day, Paleo is very doable. For someone who runs more often or longer distances, I don’t know what to tell you. I don’t have first-hand experience with that, and I don’t want to lead you down the wrong path. If you do find out, though, let me know. I’d be interested to find out from someone who is Paleo and is doing long distance running.